Many analyses of ecological networks in recent years have introduced new indices to describe network properties. As a consequence, tens of indices are available to address similar questions, differing in specific detail, sensitivity in detecting the property in question, and robustness with respect to network size and sampling intensity. Furthermore, some indices merely reflect the number of species participating in a network, but not their interrelationship, requiring a null model approach. Here we introduce a new, free software calculating a large spectrum of network indices, visualizing bipartite networks and generating null models. We use this tool to explore the sensitivity of 26 network indices to network dimensions, sampling intensity and singleton observations. Based on observed data, we investigate the interrelationship of these indices, and show that they are highly correlated, and heavily influenced by network dimensions and connectance. Finally, we re-evaluate five common hypotheses about network properties, comparing 19 pollination networks with three differently complex null models: 1. The number of links per species ("degree") follow (truncated) power law distributions. 2. Generalist pollinators interact with specialist plants, and vice versa (dependence asymmetry). 3. Ecological networks are nested. 4. Pollinators display complementarity, owing to specialization within the network. 5. Plant-pollinator networks are more robust to extinction than random networks. Our results indicate that while some hypotheses hold up against our null models, others are to a large extent understandable on the basis of network size, rather than ecological interrelationships. In particular, null model pattern of dependence asymmetry and robustness to extinction are opposite to what current network paradigms suggest. Our analysis, and the tools we provide, enables ecologists to readily contrast their findings with null model expectations for many different questions, thus separating statistical inevitability from ecological process.

Summary 1.A fundamental goal of ecological network research is to understand how the complexity observed in nature can persist and how this affects ecosystem functioning. This is essential for us to be able to predict, and eventually mitigate, the consequences of increasing environmental perturbations such as habitat loss, climate change, and invasions of exotic species. 2. Ecological networks can be subdivided into three broad types: 'traditional' food webs, mutualistic networks and host-parasitoid networks. There is a recent trend towards cross-comparisons among network types and also to take a more mechanistic, as opposed to phenomenological, perspective. For example, analysis of network configurations, such as compartments, allows us to explore the role of co-evolution in structuring mutualistic networks and host-parasitoid networks, and of body size in food webs. 3. Research into ecological networks has recently undergone a renaissance, leading to the production of a new catalogue of evermore complete, taxonomically resolved, and quantitative data. Novel topological patterns have been unearthed and it is increasingly evident that it is the distribution of interaction strengths and the configuration of complexity, rather than just its magnitude, that governs network stability and structure. 4. Another significant advance is the growing recognition of the importance of individual traits and behaviour: interactions, after all, occur between individuals. The new generation of high-quality networks is now enabling us to move away from describing networks based on species-averaged data and to start exploring patterns based on individuals. Such refinements will enable us to address more general ecological questions relating to foraging theory and the recent metabolic theory of ecology. 5. We conclude by suggesting a number of 'dead ends' and 'fruitful avenues' for future research into ecological networks.

Recent reports on local extinctions of arthropod species1 and of massive declines in arthropod biomass 2 point to land-use intensification as a major driver of decreasing biodiversity. However, there are no multi-site time-series of arthropod occurrences across land-use intensity gradients to confirm causal relationships. Moreover, it remains unclear which land-use types and arthropod groups are affected and whether the observed declines in biomass and diversity are linked to one another and continue. Here we analyzed arthropod data on more than 1 million individuals and 2,700 species from standardized inventories from 2008 to 2017 at 150 grassland and 140 forest sites in three regions of Germany. Overall gamma diversity in grasslands and forests decreased over time indicating loss of species across sites and regions. In annually sampled grasslands, biomass, abundance and species number of arthropods declined by 67%, 78%, and 34%, respectively. The decline was consistent across trophic levels, mainly affected rare species, and its magnitude was independent of local land-use intensity. However, sites embedded in landscapes with higher cover of agricultural land showed a stronger temporal decline. In 30 forest sites with annual inventories, biomass and species number, but not abundance, decreased by 41% and 36%, respectively. This was supported by analyses of all forest sites sampled in 3year intervals. The decline affected rare and abundant species and trends differed across trophic levels. Our results show that there are widespread declines in arthropods that concern biomass, abundance and diversity across trophic levels. Declines in forests demonstrate that arthropod loss is not restricted to open habitats. Our results 4 suggest that major drivers of arthropod decline act at larger spatial scales, and are, at least for grasslands, associated with agriculture at the landscape level.This implies that land-use relevant policies need to address the landscape scale to mitigate negative effects of land-use practices. Main textMuch of the debate on the human-induced biodiversity crisis has focused on vertebrates 3 , yet population decline and extinctions may be even more substantial in small organisms such as terrestrial arthropods 4 . Recent studies report declines in biomass of flying insects 2 , diversity of insect pollinators 5,6 , butterflies and moths 1,7-10 , hemipterans 11,12 and beetles 7,13,14 . Owing to the associated negative effects on food webs 15 , ecosystem functioning and ecosystem services 16 , the insect loss has spurred an intense public debate. However, time-series data on arthropods are rather limited and studies have so far focused on a small range of taxa 11,13,14 , few land-use and habitat types 12 or even on single sites 1,17 . In addition, many studies lack species information 2 or high temporal resolution 2,12 . Hence, it remains unclear whether reported declines in arthropods are a general phenomenon that is driven by similar mechanisms across land-use types, taxa and functional groups.The ...

BackgroundNetwork analyses of plant-animal interactions hold valuable biological information. They are often used to quantify the degree of specialization between partners, but usually based on qualitative indices such as 'connectance' or number of links. These measures ignore interaction frequencies or sampling intensity, and strongly depend on network size.ResultsHere we introduce two quantitative indices using interaction frequencies to describe the degree of specialization, based on information theory. The first measure (d') describes the degree of interaction specialization at the species level, while the second measure (H2') characterizes the degree of specialization or partitioning among two parties in the entire network. Both indices are mathematically related and derived from Shannon entropy. The species-level index d' can be used to analyze variation within networks, while H2' as a network-level index is useful for comparisons across different interaction webs. Analyses of two published pollinator networks identified differences and features that have not been detected with previous approaches. For instance, plants and pollinators within a network differed in their average degree of specialization (weighted mean d'), and the correlation between specialization of pollinators and their relative abundance also differed between the webs. Rarefied sampling effort in both networks and null model simulations suggest that H2' is not affected by network size or sampling intensity.ConclusionQuantitative analyses reflect properties of interaction networks more appropriately than previous qualitative attempts, and are robust against variation in sampling intensity, network size and symmetry. These measures will improve our understanding of patterns of specialization within and across networks from a broad spectrum of biological interactions.

The aim in this paper is to offer an overview of the mechanisms influencing the structure of plant-animal mutualistic networks. A brief summary is presented of the salient network patterns, the potential mechanisms are discussed and the studies that have evaluated them are reviewed. This review shows that researchers of plant-animal mutualisms have made substantial progress in the understanding of the processes behind the patterns observed in mutualistic networks. At the same time, we are still far from a thorough, integrative mechanistic understanding. We close with specific suggestions for directions of future research, which include developing methods to evaluate the relative importance of mechanisms influencing network patterns and focusing research efforts on selected representative study systems throughout the world.